Barnier also outlined a two-step negotiation timetable to ensure an orderly withdrawal for Britain, which put the future EU-Britain relations, particularly trade ties, in the second phase.
Terms of reference agreed by both sides envisage four rounds of talks on the first phase of discussions, in the weeks starting July 17, August 28, September 18 and October 9, implying trade talks are unlikely to open until after the European Council summit in October. With or without a deal, Britain will be out of the European Union on March 30, 2019.
Promising details on Monday, May also said those European Union citizens who had lived in Britain for five years could stay for life.
She made it clear that Britain wants reciprocal measures for the 1.5 million British citizens living in the EU.
Although perhaps he was talking about a British summer in particular?
In the general election this month, the Conservative Party saw its parliamentary seats fall below a majority in the legislature.
At the first day of talks in the Belgian capital, roughly a year after the UK's Brexit referendum, Mr Barnier made clear they would proceed according to the timetable set by the European Union, under which progress on the terms of withdrawal must be made before any discussions on a future trading relationship.
It's possible for the European Union (EU) and Britain to strike a fair Brexit deal which is "far better than no deal", an EU official said.
The talks will address a number of issues, including how much money Britain will owe the political and economic union, the rights of British citizens in the EU and EU citizens in Britain, and how to minimize the effects of the split on the fragile peace between Northern Ireland and Ireland.
She had called the early vote herself, saying it was to strengthen her mandate in the Brexit talks.
Bank of England Governor Mark Carney, in a speech at London's Mansion House on Tuesday, said domestic inflation pressures remain subdued and signaled he isn't in a hurry to raise interest rates.
Davis said Britain hadn't backed down.
But Merkel said that "for me, shaping the future of the 27 member states has priority over the question of the negotiations with Britain on its exit".
"It is a first good step which we appreciate", said Austrian Chancellor Christian Kern.
This would provide a "smooth path" from "where we are now" to where the United Kingdom would end up post-Brexit, he said.
"The other problem in parallel with that is that without creating a new hard border, at the same time we have to come up with solutions - especially for goods and services - but in a way that is compliant with the normal rules and integrity of the internal market", he said.
"We agreed that our closest collaborators will start a dialogue on Ireland". Michel insisted the British people had chosen to leave and negotiations should now proceed apace.
He and others have also raised the possibility that Britain could remain in the EU. If its assessment is positive, the talks will then move on to "scoping the future relationship on trade and other matters".style="text-align: center;"